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Block #315,129

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2013, 8:43:16 AM Β· Difficulty 10.0860 Β· 6,526,981 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
39280a090affa47d105bc9cce42b258c809f345cbd187bb3dac1503b95d5d476
View on Chainz β†—

Height

#315,129

Difficulty

10.085952

Transactions

1

Size

205 B

Version

2

Bits

0a1600ee

Nonce

97,269

Timestamp

12/16/2013, 8:43:16 AM

Confirmations

6,526,981

Merkle Root

a1c5cbc16d8f34e31b026149a469f8890e5aa100aa5f217c0ceaed49be6fe9ba
Transactions (1)
Coinbasea1c5cbc16d8f34…eaed49be6fe9ba
1 in β†’ 1 out9.8200 XPM116 B
AbwWkWZt…kawDhufa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.213 Γ— 10⁹²(93-digit number)
82136687247625509711…10799888726629552640
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
8.213 Γ— 10⁹²(93-digit number)
82136687247625509711…10799888726629552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.642 Γ— 10⁹³(94-digit number)
16427337449525101942…21599777453259105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.285 Γ— 10⁹³(94-digit number)
32854674899050203884…43199554906518210561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.570 Γ— 10⁹³(94-digit number)
65709349798100407768…86399109813036421121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.314 Γ— 10⁹⁴(95-digit number)
13141869959620081553…72798219626072842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.628 Γ— 10⁹⁴(95-digit number)
26283739919240163107…45596439252145684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.256 Γ— 10⁹⁴(95-digit number)
52567479838480326215…91192878504291368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.051 Γ— 10⁹⁡(96-digit number)
10513495967696065243…82385757008582737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.102 Γ— 10⁹⁡(96-digit number)
21026991935392130486…64771514017165475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.205 Γ— 10⁹⁡(96-digit number)
42053983870784260972…29543028034330951681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 315129

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 39280a090affa47d105bc9cce42b258c809f345cbd187bb3dac1503b95d5d476

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #315,129 on Chainz β†—
Circulating Supply:57,981,268 XPMΒ·at block #6,842,109 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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